profit or loss or nothing??????

Question

If two person sells banana at different rates, one for 2 for 5$ and other for 3 for 5$. If one peson is sick and other have to sell whole bananas, and he sell them for 5 (2+3) for 10$ (5$+5$). Will he gain, loose or nothing will hapen.

Answer 1

Okay, I think this is what you're asking: suppose merchant A sells 2 bananas for $5 and merchant B sells 3 bananas for $5. Then one of the merchants gets sick and the other switches to selling 5 bananas for $10, will the other mechant make more or less oney than if he had sold at his original price?

If merchant A sells at 5 for $10, he will lose money.
If merchant B sells at 5 for $10, he will gain money.

Just compute the amount each merchant makes per banana - Merchant A makes $2.50/banana and merchant B makes $1.67/banana (rounded to nearest cent). If they sell 5 for $10, they would make $2/banana.

Answer 2

it depends . . .

Say that there are x people who buy 2 bananas for $5 and y people who buy 3 bananas for $5. Then the total profit would be 5x+5y dollars for 2x+3y bananas. Thus the average cost of each banana is 5(x+y)/(2x+3y) dollars.

Now assume that the same people buy the new choice of bananas. Thus there will be 5(x+y) bananas sold for 10(x+y) dollars. Thus the average cost for banana would be 10(x+y)/[5(x+y)]=2 dollars.

When x>y>=0, then x+(4x+5y)=5(x+y)>y+(4x+5y)=2(2x+3y). Therefore 5(x+y)/(2x+3y)>2. Thus they make more money.

When y>x>=0, then 5(x+y)<2(2x+3y). Thus 5(x+y)/(2x+3y)<2, and they make less money.

When x=y>0, then 5(x+y)=10x, and 2x+3y=5x. Therefore 5(x+y)/(2x+3y)=10x/5x=2, so they make the same amount of money.

So, to reiterate (assuming the same people buy the bananas:

By average:

They will make more money if there were more people who bought the 3 bananas for $5, than there were people who only bought 2 originally.

The will make less money if there were less people who bought the 3 bananas than the 2 bananas originally.

And they will make the same money if the same number of people bought 2 bananas and 3 bananas originally.
I hope that explains it.